# Question #c4ed5

Nov 11, 2016

We know $\text{ } R = \rho \frac{L}{A} \ldots . \left(1\right)$

Where R represents the resistance of an ohmic conductor of length l and cross sectional area A and $\rho$ represents the resistivity of the material of the conductor.

Now we consider the situation when the V potential difference is applied across the ends of the conductor.Let I be the current flowing through it. In this situation the electric field acting with in the conductor is $E = \frac{V}{L}$. The current density is $i = \frac{I}{A}$

Multiplying both sides of (1) by I we get

$\implies I R = \rho \frac{L I}{A}$

By ohm's law $I R = V$

$\implies \frac{V}{L} = \rho \frac{I}{A}$

$\implies E = \rho i$

This equation shows that resistivity ($\rho$) is the proportionality constant for current density (i) and electric field (E).